Not applicable.
This invention relates to a method and apparatus used for determining the dielectric properties of materials, in particular the complex permittivity (xcex5) and loss tangent (tan xcex4).
The ultimate importance of determining the complex permittivity and loss tangent of materials over frequency is to better predict the behavior of signals propagating along a transmission line, bond wire, or nearly any type of waveguide. Knowledge of propagation speed and attenuation is key to many circuit designs. In high-speed digital applications, knowing the behavior of the complex permittivity over a frequency range is the key to predicting dispersion. Signal integrity can be better understood by examining each Fourier component.
There are several different types of test methods that have been invented over the years for determining the complex permittivity and loss tangent of dielectric materials. Most use complicated fixtures, specialized test equipment and software. All methods employ their own special equations for computational purposes.
One common method for determining the complex permittivity is called the T/R method. Weir (1) and Barry (2) provide method details. In essence, the measurement setup consists of a slab of dielectric material inserted into an air-filled coax transmission line or waveguide. An analyzer is used to perform 2 port measurements on this setup and provides the electrical signals as well as the measurement capability. Based on a set of boundary conditions and the four sets of s-parameters, the transmission and reflection coefficients are solved at the dielectric interface. Based on these parameters, equations are constructed for the complex permittivity and permeability. Information about the sample dimensions and location within the test line must be provided as well.
There are drawbacks to this method. First, the test samples must be machined to precise shapes. For coaxial fixtures, this is rather tedious. Special numerically controlled milling capabilities are required to make the samples just the right cylindrical dimensions. But there will always remain some air gap between the dielectric and the fixture which introduces errors. When using a waveguide fixture, it restricts the measurements to very high frequencies within the narrow band of the waveguide. In both cases, multi-moding must be avoided since the T/R analysis is only valid for the fundamental mode. Another drawback of this method, is that it is a resonance method, so only certain frequencies within a band can be measured depending upon the sample dimensions and fixture size. Determining complex permittivity at different frequencies requires constructing entirely new sets of test fixtures. Another problem is that the analysis breaks down at intervals where the dielectric sample length is a multiple of a half of a wavelength. Plated materials (with metal) cannot be used.
A number of cavity resonance methods have been developed for measuring the dielectric constant. The first method, developed at the National Institute fore Standards and Technology (NIST), uses a coaxial reentry cavity (3). The test setup consists of a coaxial line with a gap in the center conductor. This gap is filled by the dielectric under test. An electric field is created in the gap. Based on field equations and boundary conditions, elaborate mode matching theory is developed and expressions for Q (1/tan xcex4) and xcex5r at resonance frequencies are developed (based on TM0m modes). Losses due to the finite conductivity of the cavity walls are accounted for. An approximate filling factor due to the partially filled cavity is given. This is an additional source of error.
The shortcomings of this method are the fact that Q and xcex5r can only be determined at resonant frequencies. In addition, this method is limited to the 100 MHz to 1 GHz band. Special machining of samples is also required. Also, unlike most methods, high loss materials cannot be characterized. This method is good for determining low losses.
The next method discussed is a cavity perturbation technique (4). The test setup consists of a resonant cavity placed on an X-band waveguide. An aperture couples energy into the cavity. This method determines Q for both loaded and unloaded cavities. An explicit expression is provided for the loss tangent and dielectric constant based on the values of Q in the loaded and unloaded case, cavity dimensions, and dielectric dimensions. Q is determined from the half-power bandwidth at each resonant frequency. The measurements are limited to the five different observed resonances of the cavity, all at five different TE1x modes. The frequencies are also limited in the X-band range of 8 to 12 GHz.
One of the most common commercial methods that is available on the market today is the HP4291A RF material impedance analyzer (5). This technique employs an RF parallel plate measurement method to measure impedance. The measurement setup consists of an HP16453A test fixture that sandwiches material between two electrodes to form a dielectric filled capacitor. An independent test system, known as the HP4291A, measures the admittance of this capacitor over frequency, and the internal firmware calculates the complex permittivity {circumflex over (xcex5)}r based on the following equation:                     ϵ        ^            r        =                                        Y            m                    ⁢          t                          j          ⁢                      xe2x80x83                    ⁢                      ωϵ            0                    ⁢          A                    =                        ϵ          r          xe2x80x2                +                  j          ⁢                      xe2x80x83                    ⁢                      ϵ            r            xe2x80x3                                ,
where Ym=G+jxcfx89C is the measured admittance, xcex50 is the absolute permittivity of free space, t is the material thickness, and A is the capacitor""s plate area. The HP4291A measurement system employs an RF system to measure admittance (voltage÷current). An RF synthesized source is placed in series with the capacitor. A voltmeter placed in parallel with the source measures its complex input signal (V) while a voltmeter placed across a test resistor in series with the capacitor to determine the current (I) through it.
Calibration and fixture compensation routines are required prior to measurements. However, the method may not work for materials that are metallized. The measurement system, software, and test fixtures are very expensive as well. A couple of other fixtures can be purchased with this instrument for the low frequency measurements. This measurement system is limited to 1.5 GHz and subject to air gap errors between the test fixture and the MUT.
The present invention consists of an apparatus (with software) with the following components:
(a) a TEM or quasi-TEM test fixture;
(b) a set of unique reflective load assemblies, each having a different impedance value;
(c) an s-parameter analyzer (analyzer) that is used to make one port s-parameter measurements of either the test fixture, reflective load assembly, or calibration standards;
(d) a custom calibration kit for establishing the reference plane at the input connectorxe2x80x94fixture interface;
(e) one computer used for data acquisition, format data conversion, determining internal reflection coefficients within the system, curve fitting software, and computing complex permittivity;
(f) a second computer which is sometimes internal to the analyzer used for controlling and calibration of the analyzer;
and is used to determine the frequency dependent complex permittivity of dielectric materials by performing the following steps:
(g) assembly of test fixture with MUT;
(h) sequentially placing a set of reflective load assemblies to the analyzer and measuring s-parameters;
(i) sequentially placing the set of reflective load assemblies to the output coaxial connector on the test fixture and measuring s-parameters on the input coaxial connector;
(j) computation of the internal reflection coefficients within the test fixture based on the s-parameter measurements;
(k) de-embedding and mathematical curve-fitting to a specified electrical model of the transmission line;
(l) computation of the complex permittivity of the MUT based on the calculated impedance of elements in the specified electrical model.
This patent possesses good attributes. Several objects and advantages of this present invention are:
(a) to provide complex permittivity information over a wide frequency range which is not limited to just a few frequency points;
(b) to eliminate the need for a complex fixture design that is common with so many measurement methods;
(c) to allow users to employ any transmission line test fixture since the method will work with a transmission line of any cross sectional geometry;
(d) to provide the capability of making measurements using test equipment that is already common to many electrical laboratories;
(e) to provide the capability of determining the complex permittivity of not only solids, but liquids and gasses as well;
(f) to allow for the calibration reference plane to be placed at the end of the test fixture when using a microstrip, stripline, or coaxial test fixture for accurate measurement results;
(g) to allow one to place the dielectric under test in actual xe2x80x98in circuitxe2x80x99 test conditions;
(h) to allow one to be able to perform easy temperature testing of the dielectric.